// Copyright (c) 2022. Eritque arcus and contributors.
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU Affero General Public License as
// published by the Free Software Foundation, either version 3 of the
// License, or any later version(in your opinion).
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU Affero General Public License for more details.
//
// You should have received a copy of the GNU Affero General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.
//

#pragma once

#include <array>       // array
#include <cmath>       // signbit, isfinite
#include <cstdint>     // intN_t, uintN_t
#include <cstring>     // memcpy, memmove
#include <limits>      // numeric_limits
#include <type_traits> // conditional

#include <nlohmann/detail/macro_scope.hpp>

NLOHMANN_JSON_NAMESPACE_BEGIN
namespace detail {

    /*!
@brief implements the Grisu2 algorithm for binary to decimal floating-point
conversion.

This implementation is a slightly modified version of the reference
implementation which may be obtained from
http://florian.loitsch.com/publications (bench.tar.gz).

The code is distributed under the MIT license, Copyright (c) 2009 Florian Loitsch.

For a detailed description of the algorithm see:

[1] Loitsch, "Printing Floating-Point Numbers Quickly and Accurately with
    Integers", Proceedings of the ACM SIGPLAN 2010 Conference on Programming
    Language Design and Implementation, PLDI 2010
[2] Burger, Dybvig, "Printing Floating-Point Numbers Quickly and Accurately",
    Proceedings of the ACM SIGPLAN 1996 Conference on Programming Language
    Design and Implementation, PLDI 1996
*/
    namespace dtoa_impl {

        template<typename Target, typename Source>
        Target reinterpret_bits(const Source source) {
            static_assert(sizeof(Target) == sizeof(Source), "size mismatch");

            Target target;
            std::memcpy(&target, &source, sizeof(Source));
            return target;
        }

        struct diyfp // f * 2^e
        {
            static constexpr int kPrecision = 64; // = q

            std::uint64_t f = 0;
            int e = 0;

            constexpr diyfp(std::uint64_t f_, int e_) noexcept : f(f_), e(e_) {}

            /*!
    @brief returns x - y
    @pre x.e == y.e and x.f >= y.f
    */
            static diyfp sub(const diyfp &x, const diyfp &y) noexcept {
                JSON_ASSERT(x.e == y.e);
                JSON_ASSERT(x.f >= y.f);

                return {x.f - y.f, x.e};
            }

            /*!
    @brief returns x * y
    @note The result is rounded. (Only the upper q bits are returned.)
    */
            static diyfp mul(const diyfp &x, const diyfp &y) noexcept {
                static_assert(kPrecision == 64, "internal error");

                // Computes:
                //  f = round((x.f * y.f) / 2^q)
                //  e = x.e + y.e + q

                // Emulate the 64-bit * 64-bit multiplication:
                //
                // p = u * v
                //   = (u_lo + 2^32 u_hi) (v_lo + 2^32 v_hi)
                //   = (u_lo v_lo         ) + 2^32 ((u_lo v_hi         ) + (u_hi v_lo         )) + 2^64 (u_hi v_hi         )
                //   = (p0                ) + 2^32 ((p1                ) + (p2                )) + 2^64 (p3                )
                //   = (p0_lo + 2^32 p0_hi) + 2^32 ((p1_lo + 2^32 p1_hi) + (p2_lo + 2^32 p2_hi)) + 2^64 (p3                )
                //   = (p0_lo             ) + 2^32 (p0_hi + p1_lo + p2_lo                      ) + 2^64 (p1_hi + p2_hi + p3)
                //   = (p0_lo             ) + 2^32 (Q                                          ) + 2^64 (H                 )
                //   = (p0_lo             ) + 2^32 (Q_lo + 2^32 Q_hi                           ) + 2^64 (H                 )
                //
                // (Since Q might be larger than 2^32 - 1)
                //
                //   = (p0_lo + 2^32 Q_lo) + 2^64 (Q_hi + H)
                //
                // (Q_hi + H does not overflow a 64-bit int)
                //
                //   = p_lo + 2^64 p_hi

                const std::uint64_t u_lo = x.f & 0xFFFFFFFFu;
                const std::uint64_t u_hi = x.f >> 32u;
                const std::uint64_t v_lo = y.f & 0xFFFFFFFFu;
                const std::uint64_t v_hi = y.f >> 32u;

                const std::uint64_t p0 = u_lo * v_lo;
                const std::uint64_t p1 = u_lo * v_hi;
                const std::uint64_t p2 = u_hi * v_lo;
                const std::uint64_t p3 = u_hi * v_hi;

                const std::uint64_t p0_hi = p0 >> 32u;
                const std::uint64_t p1_lo = p1 & 0xFFFFFFFFu;
                const std::uint64_t p1_hi = p1 >> 32u;
                const std::uint64_t p2_lo = p2 & 0xFFFFFFFFu;
                const std::uint64_t p2_hi = p2 >> 32u;

                std::uint64_t Q = p0_hi + p1_lo + p2_lo;

                // The full product might now be computed as
                //
                // p_hi = p3 + p2_hi + p1_hi + (Q >> 32)
                // p_lo = p0_lo + (Q << 32)
                //
                // But in this particular case here, the full p_lo is not required.
                // Effectively we only need to add the highest bit in p_lo to p_hi (and
                // Q_hi + 1 does not overflow).

                Q += std::uint64_t{1} << (64u - 32u - 1u); // round, ties up

                const std::uint64_t h = p3 + p2_hi + p1_hi + (Q >> 32u);

                return {h, x.e + y.e + 64};
            }

            /*!
    @brief normalize x such that the significand is >= 2^(q-1)
    @pre x.f != 0
    */
            static diyfp normalize(diyfp x) noexcept {
                JSON_ASSERT(x.f != 0);

                while ((x.f >> 63u) == 0) {
                    x.f <<= 1u;
                    x.e--;
                }

                return x;
            }

            /*!
    @brief normalize x such that the result has the exponent E
    @pre e >= x.e and the upper e - x.e bits of x.f must be zero.
    */
            static diyfp normalize_to(const diyfp &x, const int target_exponent) noexcept {
                const int delta = x.e - target_exponent;

                JSON_ASSERT(delta >= 0);
                JSON_ASSERT(((x.f << delta) >> delta) == x.f);

                return {x.f << delta, target_exponent};
            }
        };

        struct boundaries {
            diyfp w;
            diyfp minus;
            diyfp plus;
        };

        /*!
Compute the (normalized) diyfp representing the input number 'value' and its
boundaries.

@pre value must be finite and positive
*/
        template<typename FloatType>
        boundaries compute_boundaries(FloatType value) {
            JSON_ASSERT(std::isfinite(value));
            JSON_ASSERT(value > 0);

            // Convert the IEEE representation into a diyfp.
            //
            // If v is denormal:
            //      value = 0.F * 2^(1 - bias) = (          F) * 2^(1 - bias - (p-1))
            // If v is normalized:
            //      value = 1.F * 2^(E - bias) = (2^(p-1) + F) * 2^(E - bias - (p-1))

            static_assert(std::numeric_limits<FloatType>::is_iec559,
                          "internal error: dtoa_short requires an IEEE-754 floating-point implementation");

            constexpr int kPrecision = std::numeric_limits<FloatType>::digits; // = p (includes the hidden bit)
            constexpr int kBias = std::numeric_limits<FloatType>::max_exponent - 1 + (kPrecision - 1);
            constexpr int kMinExp = 1 - kBias;
            constexpr std::uint64_t kHiddenBit = std::uint64_t{1} << (kPrecision - 1); // = 2^(p-1)

            using bits_type = typename std::conditional<kPrecision == 24, std::uint32_t, std::uint64_t>::type;

            const auto bits = static_cast<std::uint64_t>(reinterpret_bits<bits_type>(value));
            const std::uint64_t E = bits >> (kPrecision - 1);
            const std::uint64_t F = bits & (kHiddenBit - 1);

            const bool is_denormal = E == 0;
            const diyfp v = is_denormal
                                    ? diyfp(F, kMinExp)
                                    : diyfp(F + kHiddenBit, static_cast<int>(E) - kBias);

            // Compute the boundaries m- and m+ of the floating-point value
            // v = f * 2^e.
            //
            // Determine v- and v+, the floating-point predecessor and successor if v,
            // respectively.
            //
            //      v- = v - 2^e        if f != 2^(p-1) or e == e_min                (A)
            //         = v - 2^(e-1)    if f == 2^(p-1) and e > e_min                (B)
            //
            //      v+ = v + 2^e
            //
            // Let m- = (v- + v) / 2 and m+ = (v + v+) / 2. All real numbers _strictly_
            // between m- and m+ round to v, regardless of how the input rounding
            // algorithm breaks ties.
            //
            //      ---+-------------+-------------+-------------+-------------+---  (A)
            //         v-            m-            v             m+            v+
            //
            //      -----------------+------+------+-------------+-------------+---  (B)
            //                       v-     m-     v             m+            v+

            const bool lower_boundary_is_closer = F == 0 && E > 1;
            const diyfp m_plus = diyfp(2 * v.f + 1, v.e - 1);
            const diyfp m_minus = lower_boundary_is_closer
                                          ? diyfp(4 * v.f - 1, v.e - 2)  // (B)
                                          : diyfp(2 * v.f - 1, v.e - 1); // (A)

            // Determine the normalized w+ = m+.
            const diyfp w_plus = diyfp::normalize(m_plus);

            // Determine w- = m- such that e_(w-) = e_(w+).
            const diyfp w_minus = diyfp::normalize_to(m_minus, w_plus.e);

            return {diyfp::normalize(v), w_minus, w_plus};
        }

        // Given normalized diyfp w, Grisu needs to find a (normalized) cached
        // power-of-ten c, such that the exponent of the product c * w = f * 2^e lies
        // within a certain range [alpha, gamma] (Definition 3.2 from [1])
        //
        //      alpha <= e = e_c + e_w + q <= gamma
        //
        // or
        //
        //      f_c * f_w * 2^alpha <= f_c 2^(e_c) * f_w 2^(e_w) * 2^q
        //                          <= f_c * f_w * 2^gamma
        //
        // Since c and w are normalized, i.e. 2^(q-1) <= f < 2^q, this implies
        //
        //      2^(q-1) * 2^(q-1) * 2^alpha <= c * w * 2^q < 2^q * 2^q * 2^gamma
        //
        // or
        //
        //      2^(q - 2 + alpha) <= c * w < 2^(q + gamma)
        //
        // The choice of (alpha,gamma) determines the size of the table and the form of
        // the digit generation procedure. Using (alpha,gamma)=(-60,-32) works out well
        // in practice:
        //
        // The idea is to cut the number c * w = f * 2^e into two parts, which can be
        // processed independently: An integral part p1, and a fractional part p2:
        //
        //      f * 2^e = ( (f div 2^-e) * 2^-e + (f mod 2^-e) ) * 2^e
        //              = (f div 2^-e) + (f mod 2^-e) * 2^e
        //              = p1 + p2 * 2^e
        //
        // The conversion of p1 into decimal form requires a series of divisions and
        // modulos by (a power of) 10. These operations are faster for 32-bit than for
        // 64-bit integers, so p1 should ideally fit into a 32-bit integer. This can be
        // achieved by choosing
        //
        //      -e >= 32   or   e <= -32 := gamma
        //
        // In order to convert the fractional part
        //
        //      p2 * 2^e = p2 / 2^-e = d[-1] / 10^1 + d[-2] / 10^2 + ...
        //
        // into decimal form, the fraction is repeatedly multiplied by 10 and the digits
        // d[-i] are extracted in order:
        //
        //      (10 * p2) div 2^-e = d[-1]
        //      (10 * p2) mod 2^-e = d[-2] / 10^1 + ...
        //
        // The multiplication by 10 must not overflow. It is sufficient to choose
        //
        //      10 * p2 < 16 * p2 = 2^4 * p2 <= 2^64.
        //
        // Since p2 = f mod 2^-e < 2^-e,
        //
        //      -e <= 60   or   e >= -60 := alpha

        constexpr int kAlpha = -60;
        constexpr int kGamma = -32;

        struct cached_power // c = f * 2^e ~= 10^k
        {
            std::uint64_t f;
            int e;
            int k;
        };

        /*!
For a normalized diyfp w = f * 2^e, this function returns a (normalized) cached
power-of-ten c = f_c * 2^e_c, such that the exponent of the product w * c
satisfies (Definition 3.2 from [1])

     alpha <= e_c + e + q <= gamma.
*/
        inline cached_power get_cached_power_for_binary_exponent(int e) {
            // Now
            //
            //      alpha <= e_c + e + q <= gamma                                    (1)
            //      ==> f_c * 2^alpha <= c * 2^e * 2^q
            //
            // and since the c's are normalized, 2^(q-1) <= f_c,
            //
            //      ==> 2^(q - 1 + alpha) <= c * 2^(e + q)
            //      ==> 2^(alpha - e - 1) <= c
            //
            // If c were an exact power of ten, i.e. c = 10^k, one may determine k as
            //
            //      k = ceil( log_10( 2^(alpha - e - 1) ) )
            //        = ceil( (alpha - e - 1) * log_10(2) )
            //
            // From the paper:
            // "In theory the result of the procedure could be wrong since c is rounded,
            //  and the computation itself is approximated [...]. In practice, however,
            //  this simple function is sufficient."
            //
            // For IEEE double precision floating-point numbers converted into
            // normalized diyfp's w = f * 2^e, with q = 64,
            //
            //      e >= -1022      (min IEEE exponent)
            //           -52        (p - 1)
            //           -52        (p - 1, possibly normalize denormal IEEE numbers)
            //           -11        (normalize the diyfp)
            //         = -1137
            //
            // and
            //
            //      e <= +1023      (max IEEE exponent)
            //           -52        (p - 1)
            //           -11        (normalize the diyfp)
            //         = 960
            //
            // This binary exponent range [-1137,960] results in a decimal exponent
            // range [-307,324]. One does not need to store a cached power for each
            // k in this range. For each such k it suffices to find a cached power
            // such that the exponent of the product lies in [alpha,gamma].
            // This implies that the difference of the decimal exponents of adjacent
            // table entries must be less than or equal to
            //
            //      floor( (gamma - alpha) * log_10(2) ) = 8.
            //
            // (A smaller distance gamma-alpha would require a larger table.)

            // NB:
            // Actually this function returns c, such that -60 <= e_c + e + 64 <= -34.

            constexpr int kCachedPowersMinDecExp = -300;
            constexpr int kCachedPowersDecStep = 8;

            static constexpr std::array<cached_power, 79> kCachedPowers =
                    {
                            {
                                    {0xAB70FE17C79AC6CA, -1060, -300},
                                    {0xFF77B1FCBEBCDC4F, -1034, -292},
                                    {0xBE5691EF416BD60C, -1007, -284},
                                    {0x8DD01FAD907FFC3C, -980, -276},
                                    {0xD3515C2831559A83, -954, -268},
                                    {0x9D71AC8FADA6C9B5, -927, -260},
                                    {0xEA9C227723EE8BCB, -901, -252},
                                    {0xAECC49914078536D, -874, -244},
                                    {0x823C12795DB6CE57, -847, -236},
                                    {0xC21094364DFB5637, -821, -228},
                                    {0x9096EA6F3848984F, -794, -220},
                                    {0xD77485CB25823AC7, -768, -212},
                                    {0xA086CFCD97BF97F4, -741, -204},
                                    {0xEF340A98172AACE5, -715, -196},
                                    {0xB23867FB2A35B28E, -688, -188},
                                    {0x84C8D4DFD2C63F3B, -661, -180},
                                    {0xC5DD44271AD3CDBA, -635, -172},
                                    {0x936B9FCEBB25C996, -608, -164},
                                    {0xDBAC6C247D62A584, -582, -156},
                                    {0xA3AB66580D5FDAF6, -555, -148},
                                    {0xF3E2F893DEC3F126, -529, -140},
                                    {0xB5B5ADA8AAFF80B8, -502, -132},
                                    {0x87625F056C7C4A8B, -475, -124},
                                    {0xC9BCFF6034C13053, -449, -116},
                                    {0x964E858C91BA2655, -422, -108},
                                    {0xDFF9772470297EBD, -396, -100},
                                    {0xA6DFBD9FB8E5B88F, -369, -92},
                                    {0xF8A95FCF88747D94, -343, -84},
                                    {0xB94470938FA89BCF, -316, -76},
                                    {0x8A08F0F8BF0F156B, -289, -68},
                                    {0xCDB02555653131B6, -263, -60},
                                    {0x993FE2C6D07B7FAC, -236, -52},
                                    {0xE45C10C42A2B3B06, -210, -44},
                                    {0xAA242499697392D3, -183, -36},
                                    {0xFD87B5F28300CA0E, -157, -28},
                                    {0xBCE5086492111AEB, -130, -20},
                                    {0x8CBCCC096F5088CC, -103, -12},
                                    {0xD1B71758E219652C, -77, -4},
                                    {0x9C40000000000000, -50, 4},
                                    {0xE8D4A51000000000, -24, 12},
                                    {0xAD78EBC5AC620000, 3, 20},
                                    {0x813F3978F8940984, 30, 28},
                                    {0xC097CE7BC90715B3, 56, 36},
                                    {0x8F7E32CE7BEA5C70, 83, 44},
                                    {0xD5D238A4ABE98068, 109, 52},
                                    {0x9F4F2726179A2245, 136, 60},
                                    {0xED63A231D4C4FB27, 162, 68},
                                    {0xB0DE65388CC8ADA8, 189, 76},
                                    {0x83C7088E1AAB65DB, 216, 84},
                                    {0xC45D1DF942711D9A, 242, 92},
                                    {0x924D692CA61BE758, 269, 100},
                                    {0xDA01EE641A708DEA, 295, 108},
                                    {0xA26DA3999AEF774A, 322, 116},
                                    {0xF209787BB47D6B85, 348, 124},
                                    {0xB454E4A179DD1877, 375, 132},
                                    {0x865B86925B9BC5C2, 402, 140},
                                    {0xC83553C5C8965D3D, 428, 148},
                                    {0x952AB45CFA97A0B3, 455, 156},
                                    {0xDE469FBD99A05FE3, 481, 164},
                                    {0xA59BC234DB398C25, 508, 172},
                                    {0xF6C69A72A3989F5C, 534, 180},
                                    {0xB7DCBF5354E9BECE, 561, 188},
                                    {0x88FCF317F22241E2, 588, 196},
                                    {0xCC20CE9BD35C78A5, 614, 204},
                                    {0x98165AF37B2153DF, 641, 212},
                                    {0xE2A0B5DC971F303A, 667, 220},
                                    {0xA8D9D1535CE3B396, 694, 228},
                                    {0xFB9B7CD9A4A7443C, 720, 236},
                                    {0xBB764C4CA7A44410, 747, 244},
                                    {0x8BAB8EEFB6409C1A, 774, 252},
                                    {0xD01FEF10A657842C, 800, 260},
                                    {0x9B10A4E5E9913129, 827, 268},
                                    {0xE7109BFBA19C0C9D, 853, 276},
                                    {0xAC2820D9623BF429, 880, 284},
                                    {0x80444B5E7AA7CF85, 907, 292},
                                    {0xBF21E44003ACDD2D, 933, 300},
                                    {0x8E679C2F5E44FF8F, 960, 308},
                                    {0xD433179D9C8CB841, 986, 316},
                                    {0x9E19DB92B4E31BA9, 1013, 324},
                            }};

            // This computation gives exactly the same results for k as
            //      k = ceil((kAlpha - e - 1) * 0.30102999566398114)
            // for |e| <= 1500, but doesn't require floating-point operations.
            // NB: log_10(2) ~= 78913 / 2^18
            JSON_ASSERT(e >= -1500);
            JSON_ASSERT(e <= 1500);
            const int f = kAlpha - e - 1;
            const int k = (f * 78913) / (1 << 18) + static_cast<int>(f > 0);

            const int index = (-kCachedPowersMinDecExp + k + (kCachedPowersDecStep - 1)) / kCachedPowersDecStep;
            JSON_ASSERT(index >= 0);
            JSON_ASSERT(static_cast<std::size_t>(index) < kCachedPowers.size());

            const cached_power cached = kCachedPowers[static_cast<std::size_t>(index)];
            JSON_ASSERT(kAlpha <= cached.e + e + 64);
            JSON_ASSERT(kGamma >= cached.e + e + 64);

            return cached;
        }

        /*!
For n != 0, returns k, such that pow10 := 10^(k-1) <= n < 10^k.
For n == 0, returns 1 and sets pow10 := 1.
*/
        inline int find_largest_pow10(const std::uint32_t n, std::uint32_t &pow10) {
            // LCOV_EXCL_START
            if (n >= 1000000000) {
                pow10 = 1000000000;
                return 10;
            }
            // LCOV_EXCL_STOP
            if (n >= 100000000) {
                pow10 = 100000000;
                return 9;
            }
            if (n >= 10000000) {
                pow10 = 10000000;
                return 8;
            }
            if (n >= 1000000) {
                pow10 = 1000000;
                return 7;
            }
            if (n >= 100000) {
                pow10 = 100000;
                return 6;
            }
            if (n >= 10000) {
                pow10 = 10000;
                return 5;
            }
            if (n >= 1000) {
                pow10 = 1000;
                return 4;
            }
            if (n >= 100) {
                pow10 = 100;
                return 3;
            }
            if (n >= 10) {
                pow10 = 10;
                return 2;
            }

            pow10 = 1;
            return 1;
        }

        inline void grisu2_round(char *buf, int len, std::uint64_t dist, std::uint64_t delta,
                                 std::uint64_t rest, std::uint64_t ten_k) {
            JSON_ASSERT(len >= 1);
            JSON_ASSERT(dist <= delta);
            JSON_ASSERT(rest <= delta);
            JSON_ASSERT(ten_k > 0);

            //               <--------------------------- delta ---->
            //                                  <---- dist --------->
            // --------------[------------------+-------------------]--------------
            //               M-                 w                   M+
            //
            //                                  ten_k
            //                                <------>
            //                                       <---- rest ---->
            // --------------[------------------+----+--------------]--------------
            //                                  w    V
            //                                       = buf * 10^k
            //
            // ten_k represents a unit-in-the-last-place in the decimal representation
            // stored in buf.
            // Decrement buf by ten_k while this takes buf closer to w.

            // The tests are written in this order to avoid overflow in unsigned
            // integer arithmetic.

            while (rest < dist && delta - rest >= ten_k && (rest + ten_k < dist || dist - rest > rest + ten_k - dist)) {
                JSON_ASSERT(buf[len - 1] != '0');
                buf[len - 1]--;
                rest += ten_k;
            }
        }

        /*!
Generates V = buffer * 10^decimal_exponent, such that M- <= V <= M+.
M- and M+ must be normalized and share the same exponent -60 <= e <= -32.
*/
        inline void grisu2_digit_gen(char *buffer, int &length, int &decimal_exponent,
                                     diyfp M_minus, diyfp w, diyfp M_plus) {
            static_assert(kAlpha >= -60, "internal error");
            static_assert(kGamma <= -32, "internal error");

            // Generates the digits (and the exponent) of a decimal floating-point
            // number V = buffer * 10^decimal_exponent in the range [M-, M+]. The diyfp's
            // w, M- and M+ share the same exponent e, which satisfies alpha <= e <= gamma.
            //
            //               <--------------------------- delta ---->
            //                                  <---- dist --------->
            // --------------[------------------+-------------------]--------------
            //               M-                 w                   M+
            //
            // Grisu2 generates the digits of M+ from left to right and stops as soon as
            // V is in [M-,M+].

            JSON_ASSERT(M_plus.e >= kAlpha);
            JSON_ASSERT(M_plus.e <= kGamma);

            std::uint64_t delta = diyfp::sub(M_plus, M_minus).f; // (significand of (M+ - M-), implicit exponent is e)
            std::uint64_t dist = diyfp::sub(M_plus, w).f;        // (significand of (M+ - w ), implicit exponent is e)

            // Split M+ = f * 2^e into two parts p1 and p2 (note: e < 0):
            //
            //      M+ = f * 2^e
            //         = ((f div 2^-e) * 2^-e + (f mod 2^-e)) * 2^e
            //         = ((p1        ) * 2^-e + (p2        )) * 2^e
            //         = p1 + p2 * 2^e

            const diyfp one(std::uint64_t{1} << -M_plus.e, M_plus.e);

            auto p1 = static_cast<std::uint32_t>(M_plus.f >> -one.e); // p1 = f div 2^-e (Since -e >= 32, p1 fits into a 32-bit int.)
            std::uint64_t p2 = M_plus.f & (one.f - 1);                // p2 = f mod 2^-e

            // 1)
            //
            // Generate the digits of the integral part p1 = d[n-1]...d[1]d[0]

            JSON_ASSERT(p1 > 0);

            std::uint32_t pow10{};
            const int k = find_largest_pow10(p1, pow10);

            //      10^(k-1) <= p1 < 10^k, pow10 = 10^(k-1)
            //
            //      p1 = (p1 div 10^(k-1)) * 10^(k-1) + (p1 mod 10^(k-1))
            //         = (d[k-1]         ) * 10^(k-1) + (p1 mod 10^(k-1))
            //
            //      M+ = p1                                             + p2 * 2^e
            //         = d[k-1] * 10^(k-1) + (p1 mod 10^(k-1))          + p2 * 2^e
            //         = d[k-1] * 10^(k-1) + ((p1 mod 10^(k-1)) * 2^-e + p2) * 2^e
            //         = d[k-1] * 10^(k-1) + (                         rest) * 2^e
            //
            // Now generate the digits d[n] of p1 from left to right (n = k-1,...,0)
            //
            //      p1 = d[k-1]...d[n] * 10^n + d[n-1]...d[0]
            //
            // but stop as soon as
            //
            //      rest * 2^e = (d[n-1]...d[0] * 2^-e + p2) * 2^e <= delta * 2^e

            int n = k;
            while (n > 0) {
                // Invariants:
                //      M+ = buffer * 10^n + (p1 + p2 * 2^e)    (buffer = 0 for n = k)
                //      pow10 = 10^(n-1) <= p1 < 10^n
                //
                const std::uint32_t d = p1 / pow10; // d = p1 div 10^(n-1)
                const std::uint32_t r = p1 % pow10; // r = p1 mod 10^(n-1)
                //
                //      M+ = buffer * 10^n + (d * 10^(n-1) + r) + p2 * 2^e
                //         = (buffer * 10 + d) * 10^(n-1) + (r + p2 * 2^e)
                //
                JSON_ASSERT(d <= 9);
                buffer[length++] = static_cast<char>('0' + d); // buffer := buffer * 10 + d
                //
                //      M+ = buffer * 10^(n-1) + (r + p2 * 2^e)
                //
                p1 = r;
                n--;
                //
                //      M+ = buffer * 10^n + (p1 + p2 * 2^e)
                //      pow10 = 10^n
                //

                // Now check if enough digits have been generated.
                // Compute
                //
                //      p1 + p2 * 2^e = (p1 * 2^-e + p2) * 2^e = rest * 2^e
                //
                // Note:
                // Since rest and delta share the same exponent e, it suffices to
                // compare the significands.
                const std::uint64_t rest = (std::uint64_t{p1} << -one.e) + p2;
                if (rest <= delta) {
                    // V = buffer * 10^n, with M- <= V <= M+.

                    decimal_exponent += n;

                    // We may now just stop. But instead look if the buffer could be
                    // decremented to bring V closer to w.
                    //
                    // pow10 = 10^n is now 1 ulp in the decimal representation V.
                    // The rounding procedure works with diyfp's with an implicit
                    // exponent of e.
                    //
                    //      10^n = (10^n * 2^-e) * 2^e = ulp * 2^e
                    //
                    const std::uint64_t ten_n = std::uint64_t{pow10} << -one.e;
                    grisu2_round(buffer, length, dist, delta, rest, ten_n);

                    return;
                }

                pow10 /= 10;
                //
                //      pow10 = 10^(n-1) <= p1 < 10^n
                // Invariants restored.
            }

            // 2)
            //
            // The digits of the integral part have been generated:
            //
            //      M+ = d[k-1]...d[1]d[0] + p2 * 2^e
            //         = buffer            + p2 * 2^e
            //
            // Now generate the digits of the fractional part p2 * 2^e.
            //
            // Note:
            // No decimal point is generated: the exponent is adjusted instead.
            //
            // p2 actually represents the fraction
            //
            //      p2 * 2^e
            //          = p2 / 2^-e
            //          = d[-1] / 10^1 + d[-2] / 10^2 + ...
            //
            // Now generate the digits d[-m] of p1 from left to right (m = 1,2,...)
            //
            //      p2 * 2^e = d[-1]d[-2]...d[-m] * 10^-m
            //                      + 10^-m * (d[-m-1] / 10^1 + d[-m-2] / 10^2 + ...)
            //
            // using
            //
            //      10^m * p2 = ((10^m * p2) div 2^-e) * 2^-e + ((10^m * p2) mod 2^-e)
            //                = (                   d) * 2^-e + (                   r)
            //
            // or
            //      10^m * p2 * 2^e = d + r * 2^e
            //
            // i.e.
            //
            //      M+ = buffer + p2 * 2^e
            //         = buffer + 10^-m * (d + r * 2^e)
            //         = (buffer * 10^m + d) * 10^-m + 10^-m * r * 2^e
            //
            // and stop as soon as 10^-m * r * 2^e <= delta * 2^e

            JSON_ASSERT(p2 > delta);

            int m = 0;
            for (;;) {
                // Invariant:
                //      M+ = buffer * 10^-m + 10^-m * (d[-m-1] / 10 + d[-m-2] / 10^2 + ...) * 2^e
                //         = buffer * 10^-m + 10^-m * (p2                                 ) * 2^e
                //         = buffer * 10^-m + 10^-m * (1/10 * (10 * p2)                   ) * 2^e
                //         = buffer * 10^-m + 10^-m * (1/10 * ((10*p2 div 2^-e) * 2^-e + (10*p2 mod 2^-e)) * 2^e
                //
                JSON_ASSERT(p2 <= (std::numeric_limits<std::uint64_t>::max)() / 10);
                p2 *= 10;
                const std::uint64_t d = p2 >> -one.e;     // d = (10 * p2) div 2^-e
                const std::uint64_t r = p2 & (one.f - 1); // r = (10 * p2) mod 2^-e
                //
                //      M+ = buffer * 10^-m + 10^-m * (1/10 * (d * 2^-e + r) * 2^e
                //         = buffer * 10^-m + 10^-m * (1/10 * (d + r * 2^e))
                //         = (buffer * 10 + d) * 10^(-m-1) + 10^(-m-1) * r * 2^e
                //
                JSON_ASSERT(d <= 9);
                buffer[length++] = static_cast<char>('0' + d); // buffer := buffer * 10 + d
                //
                //      M+ = buffer * 10^(-m-1) + 10^(-m-1) * r * 2^e
                //
                p2 = r;
                m++;
                //
                //      M+ = buffer * 10^-m + 10^-m * p2 * 2^e
                // Invariant restored.

                // Check if enough digits have been generated.
                //
                //      10^-m * p2 * 2^e <= delta * 2^e
                //              p2 * 2^e <= 10^m * delta * 2^e
                //                    p2 <= 10^m * delta
                delta *= 10;
                dist *= 10;
                if (p2 <= delta) {
                    break;
                }
            }

            // V = buffer * 10^-m, with M- <= V <= M+.

            decimal_exponent -= m;

            // 1 ulp in the decimal representation is now 10^-m.
            // Since delta and dist are now scaled by 10^m, we need to do the
            // same with ulp in order to keep the units in sync.
            //
            //      10^m * 10^-m = 1 = 2^-e * 2^e = ten_m * 2^e
            //
            const std::uint64_t ten_m = one.f;
            grisu2_round(buffer, length, dist, delta, p2, ten_m);

            // By construction this algorithm generates the shortest possible decimal
            // number (Loitsch, Theorem 6.2) which rounds back to w.
            // For an input number of precision p, at least
            //
            //      N = 1 + ceil(p * log_10(2))
            //
            // decimal digits are sufficient to identify all binary floating-point
            // numbers (Matula, "In-and-Out conversions").
            // This implies that the algorithm does not produce more than N decimal
            // digits.
            //
            //      N = 17 for p = 53 (IEEE double precision)
            //      N = 9  for p = 24 (IEEE single precision)
        }

        /*!
v = buf * 10^decimal_exponent
len is the length of the buffer (number of decimal digits)
The buffer must be large enough, i.e. >= max_digits10.
*/
        JSON_HEDLEY_NON_NULL(1)
        inline void grisu2(char *buf, int &len, int &decimal_exponent,
                           diyfp m_minus, diyfp v, diyfp m_plus) {
            JSON_ASSERT(m_plus.e == m_minus.e);
            JSON_ASSERT(m_plus.e == v.e);

            //  --------(-----------------------+-----------------------)--------    (A)
            //          m-                      v                       m+
            //
            //  --------------------(-----------+-----------------------)--------    (B)
            //                      m-          v                       m+
            //
            // First scale v (and m- and m+) such that the exponent is in the range
            // [alpha, gamma].

            const cached_power cached = get_cached_power_for_binary_exponent(m_plus.e);

            const diyfp c_minus_k(cached.f, cached.e); // = c ~= 10^-k

            // The exponent of the products is = v.e + c_minus_k.e + q and is in the range [alpha,gamma]
            const diyfp w = diyfp::mul(v, c_minus_k);
            const diyfp w_minus = diyfp::mul(m_minus, c_minus_k);
            const diyfp w_plus = diyfp::mul(m_plus, c_minus_k);

            //  ----(---+---)---------------(---+---)---------------(---+---)----
            //          w-                      w                       w+
            //          = c*m-                  = c*v                   = c*m+
            //
            // diyfp::mul rounds its result and c_minus_k is approximated too. w, w- and
            // w+ are now off by a small amount.
            // In fact:
            //
            //      w - v * 10^k < 1 ulp
            //
            // To account for this inaccuracy, add resp. subtract 1 ulp.
            //
            //  --------+---[---------------(---+---)---------------]---+--------
            //          w-  M-                  w                   M+  w+
            //
            // Now any number in [M-, M+] (bounds included) will round to w when input,
            // regardless of how the input rounding algorithm breaks ties.
            //
            // And digit_gen generates the shortest possible such number in [M-, M+].
            // Note that this does not mean that Grisu2 always generates the shortest
            // possible number in the interval (m-, m+).
            const diyfp M_minus(w_minus.f + 1, w_minus.e);
            const diyfp M_plus(w_plus.f - 1, w_plus.e);

            decimal_exponent = -cached.k; // = -(-k) = k

            grisu2_digit_gen(buf, len, decimal_exponent, M_minus, w, M_plus);
        }

        /*!
v = buf * 10^decimal_exponent
len is the length of the buffer (number of decimal digits)
The buffer must be large enough, i.e. >= max_digits10.
*/
        template<typename FloatType>
        JSON_HEDLEY_NON_NULL(1)
        void grisu2(char *buf, int &len, int &decimal_exponent, FloatType value) {
            static_assert(diyfp::kPrecision >= std::numeric_limits<FloatType>::digits + 3,
                          "internal error: not enough precision");

            JSON_ASSERT(std::isfinite(value));
            JSON_ASSERT(value > 0);

            // If the neighbors (and boundaries) of 'value' are always computed for double-precision
            // numbers, all float's can be recovered using strtod (and strtof). However, the resulting
            // decimal representations are not exactly "short".
            //
            // The documentation for 'std::to_chars' (https://en.cppreference.com/w/cpp/utility/to_chars)
            // says "value is converted to a string as if by std::sprintf in the default ("C") locale"
            // and since sprintf promotes floats to doubles, I think this is exactly what 'std::to_chars'
            // does.
            // On the other hand, the documentation for 'std::to_chars' requires that "parsing the
            // representation using the corresponding std::from_chars function recovers value exactly". That
            // indicates that single precision floating-point numbers should be recovered using
            // 'std::strtof'.
            //
            // NB: If the neighbors are computed for single-precision numbers, there is a single float
            //     (7.0385307e-26f) which can't be recovered using strtod. The resulting double precision
            //     value is off by 1 ulp.
#if 0
    const boundaries w = compute_boundaries(static_cast<double>(value));
#else
            const boundaries w = compute_boundaries(value);
#endif

            grisu2(buf, len, decimal_exponent, w.minus, w.w, w.plus);
        }

        /*!
@brief appends a decimal representation of e to buf
@return a pointer to the element following the exponent.
@pre -1000 < e < 1000
*/
        JSON_HEDLEY_NON_NULL(1)
        JSON_HEDLEY_RETURNS_NON_NULL
        inline char *append_exponent(char *buf, int e) {
            JSON_ASSERT(e > -1000);
            JSON_ASSERT(e < 1000);

            if (e < 0) {
                e = -e;
                *buf++ = '-';
            } else {
                *buf++ = '+';
            }

            auto k = static_cast<std::uint32_t>(e);
            if (k < 10) {
                // Always print at least two digits in the exponent.
                // This is for compatibility with printf("%g").
                *buf++ = '0';
                *buf++ = static_cast<char>('0' + k);
            } else if (k < 100) {
                *buf++ = static_cast<char>('0' + k / 10);
                k %= 10;
                *buf++ = static_cast<char>('0' + k);
            } else {
                *buf++ = static_cast<char>('0' + k / 100);
                k %= 100;
                *buf++ = static_cast<char>('0' + k / 10);
                k %= 10;
                *buf++ = static_cast<char>('0' + k);
            }

            return buf;
        }

        /*!
@brief prettify v = buf * 10^decimal_exponent

If v is in the range [10^min_exp, 10^max_exp) it will be printed in fixed-point
notation. Otherwise it will be printed in exponential notation.

@pre min_exp < 0
@pre max_exp > 0
*/
        JSON_HEDLEY_NON_NULL(1)
        JSON_HEDLEY_RETURNS_NON_NULL
        inline char *format_buffer(char *buf, int len, int decimal_exponent,
                                   int min_exp, int max_exp) {
            JSON_ASSERT(min_exp < 0);
            JSON_ASSERT(max_exp > 0);

            const int k = len;
            const int n = len + decimal_exponent;

            // v = buf * 10^(n-k)
            // k is the length of the buffer (number of decimal digits)
            // n is the position of the decimal point relative to the start of the buffer.

            if (k <= n && n <= max_exp) {
                // digits[000]
                // len <= max_exp + 2

                std::memset(buf + k, '0', static_cast<size_t>(n) - static_cast<size_t>(k));
                // Make it look like a floating-point number (#362, #378)
                buf[n + 0] = '.';
                buf[n + 1] = '0';
                return buf + (static_cast<size_t>(n) + 2);
            }

            if (0 < n && n <= max_exp) {
                // dig.its
                // len <= max_digits10 + 1

                JSON_ASSERT(k > n);

                std::memmove(buf + (static_cast<size_t>(n) + 1), buf + n, static_cast<size_t>(k) - static_cast<size_t>(n));
                buf[n] = '.';
                return buf + (static_cast<size_t>(k) + 1U);
            }

            if (min_exp < n && n <= 0) {
                // 0.[000]digits
                // len <= 2 + (-min_exp - 1) + max_digits10

                std::memmove(buf + (2 + static_cast<size_t>(-n)), buf, static_cast<size_t>(k));
                buf[0] = '0';
                buf[1] = '.';
                std::memset(buf + 2, '0', static_cast<size_t>(-n));
                return buf + (2U + static_cast<size_t>(-n) + static_cast<size_t>(k));
            }

            if (k == 1) {
                // dE+123
                // len <= 1 + 5

                buf += 1;
            } else {
                // d.igitsE+123
                // len <= max_digits10 + 1 + 5

                std::memmove(buf + 2, buf + 1, static_cast<size_t>(k) - 1);
                buf[1] = '.';
                buf += 1 + static_cast<size_t>(k);
            }

            *buf++ = 'e';
            return append_exponent(buf, n - 1);
        }

    } // namespace dtoa_impl

    /*!
@brief generates a decimal representation of the floating-point number value in [first, last).

The format of the resulting decimal representation is similar to printf's %g
format. Returns an iterator pointing past-the-end of the decimal representation.

@note The input number must be finite, i.e. NaN's and Inf's are not supported.
@note The buffer must be large enough.
@note The result is NOT null-terminated.
*/
    template<typename FloatType>
    JSON_HEDLEY_NON_NULL(1, 2)
    JSON_HEDLEY_RETURNS_NON_NULL
            char *to_chars(char *first, const char *last, FloatType value) {
        static_cast<void>(last); // maybe unused - fix warning
        JSON_ASSERT(std::isfinite(value));

        // Use signbit(value) instead of (value < 0) since signbit works for -0.
        if (std::signbit(value)) {
            value = -value;
            *first++ = '-';
        }

#ifdef __GNUC__
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wfloat-equal"
#endif
        if (value == 0) // +-0
        {
            *first++ = '0';
            // Make it look like a floating-point number (#362, #378)
            *first++ = '.';
            *first++ = '0';
            return first;
        }
#ifdef __GNUC__
#pragma GCC diagnostic pop
#endif

        JSON_ASSERT(last - first >= std::numeric_limits<FloatType>::max_digits10);

        // Compute v = buffer * 10^decimal_exponent.
        // The decimal digits are stored in the buffer, which needs to be interpreted
        // as an unsigned decimal integer.
        // len is the length of the buffer, i.e. the number of decimal digits.
        int len = 0;
        int decimal_exponent = 0;
        dtoa_impl::grisu2(first, len, decimal_exponent, value);

        JSON_ASSERT(len <= std::numeric_limits<FloatType>::max_digits10);

        // Format the buffer like printf("%.*g", prec, value)
        constexpr int kMinExp = -4;
        // Use digits10 here to increase compatibility with version 2.
        constexpr int kMaxExp = std::numeric_limits<FloatType>::digits10;

        JSON_ASSERT(last - first >= kMaxExp + 2);
        JSON_ASSERT(last - first >= 2 + (-kMinExp - 1) + std::numeric_limits<FloatType>::max_digits10);
        JSON_ASSERT(last - first >= std::numeric_limits<FloatType>::max_digits10 + 6);

        return dtoa_impl::format_buffer(first, len, decimal_exponent, kMinExp, kMaxExp);
    }

} // namespace detail
NLOHMANN_JSON_NAMESPACE_END
